II. ABSTRACT FAR INFRARED ABSORPTION IN THIN FILMS 0F PURE AND MIXED ALKALI HALIDES I ‘ in by Richard M? fUller Experimental techniques were developed for the preparation and observation of thin evaporated films of pure alkali halides and of mixtures of alkali halides. Spectra were obtained in the neighborhood of strong infrared absorption. From the spectra the infrared dispersion frequency and the damping constant were obtained for the pure alkali halides. For Lil, the only alkali halide for which the infrared dispersion frequency had been measured neither by reflection or transmission, this parameter was found to be 144 cm'l. For the other alkali halides, the values obtained were in very good agreement with those observed earlier by others in transmission measurements, and in good agreement with those deduced earlier from reflection measurements.' The data are used to get a value of the effective charge e* according to Szigeti's formula. A correlation appears to exist between values of damping constant and deviation of e*/e from unity. Agreement between experimental values of e*/e and those predicted by theory can be said to be only fair. With mixed films, composed of various proportions of LiBr with NaBr, LiCl with LiBr, and NaI with K1, the absorption spectra tended to have complex shapes, and only the infrared dispersion frequency could be determined. This parameter changes with composition and temperature. ‘ The dispersion frequency shows a larger shift for a small proportion of the heavier component than that observed when the light constituent is the minority component. Also the absorption bands show much more broadening for the heavy minority component films than for light minority component films. For all of the systems studied, the absorption minimum becomes very broad and poorly defined as 50%—50% compositions are approached. ‘The low temperature data from the NaI-KI system shows much sharper absorption at liquid-nitrogen temperatures as well as a shift of the dispersion frequency to higher values. For the LiCl-LiBr system at intermediate compositions, a single band appears immediately after evaporation. Presently, the initial peak disappears and a new broader one appears with a minimum at a frequency about 60% of the initial minimum. This new minimum shifts monotonically with composition between the values of 201 cm'1 and 170 cm"1 for the pure LiCl and LiBr respectively. FAR INFRARED ABSORPTION IN THIN FILMS OF PURE AND MIXED ALKALI HALIDES By -, C. Richard M. Fuller A THESIS Submitted to Michigan State university in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Physics and Astronomy 1965 ll ACKNOWLEDGMENTS Just as this thesis is the written evidence of a most valuable research experience, so are these words only written evidence of a feeling of profound appreciation for the contributions of many people who made this experience possible. Dr. Donald J. Montgomery directed the work with the insight that made set backs as valuable as success. He has been an unfailing source of encouragement and counsel. The spirit of cooperation and excitement of the solid-state spectroscopy group is a tribute to the quality of leadership provided by Dr. Montgomery. Dr. Charles M. Randall has provided invaluable assistance and counsel throughout the course of this work. He initially formulated the computer program used in the spectral analysis of this thesis. The example he set in experimental research will continue to serve as a model for the author. Dr. Sitaram Jaswal was a valuable source of ideas and a sounding board for theoretical interpretations of the experimental work. Karl Zetterholm did much of the important computer programing and organizing of data for analysis. Gene Gardner punched data cards and cataloged spectra. Alma College provided tangible support and a leave of absence in order to make this work possible. The research has been supported by the Air Force Office of Scientific Research. 14' Finally, but most important, my wife, Judy, has been always a source of encouragement and has provided much assistance in the preparation of this thesis. To these people and the many others who have assisted in this work, I express my appreciation. m CHAPTER TABLE OF CONTENTS I. INTRODUCT ION O I G O O I I l O I O O O 0 II. EXPERIMENTAL APPARATUS AND TECHNIQUE . . Sample Handling . . . . . . . . . Evaporation Apparatus . . . . . . Film Preparation . . . . . . . . Transmission-Spectra Measurements Spectral Analysis . . . . . . . . III. EXPERIMENTAL RESULTS AND DISCUSSION . . REFERENCES APPENDIX Pure Film Results . . . . Mixed-Film Results . . . LiBr-NaBr System . . LiCl-LiBr System . . NaI-KI System . . . General Discussion . . . . . c Infrared Dispersion Frequen y Absorption Spectra Shape . Page U‘ LIST OF TABLES TABLE Page I. Experimental Data for Pure Films . o . . . . . 22 II. Comparison of e*/e Values . . . . o . . . o . 25 III&IV Effect of Composition on Dispersion Frequency fOI‘ NaI‘KI Films 0 I I I I I I I o I I I o 27 V&VI Effect of Composition on Dispersion Frequency for LiBI'wNaBI‘ Films I I I I I I o I I o I I I 28 JD VII & Effect of Composition on Dispersion Frequency VIII 'for LiCl‘LiBr Films I I I I I I I I I I I o I 29 FIGURE 1. 2. 3. 5. 6. 7. e. 9. 10. 11. 12. 13. 1a. 15. 16. 17. 18. 19. 20. 21. 22. LIST OF FIGURES Evaporation system . Sample cell . . . . Optical path of spectrophotometer . . . . Reference spectrum for sample cell . . . . Corrected and calculated LiBr spectrum . . Absorption spectrum Absorption spectrum Absorption spectrum Absorption spectrum Absorption spectrum Absorption spectrum Absorption spectrum Absorption spectrum Absorption spectrum Dispersion Absorption Absorptions pectrum 60% LiBr-hOSPLiC1 Absorption spectrum 60% LiBr-#05 L101 ectrum LiCl Absorptions NOS LiBr-608 Absorption spectrum 40% LiBr-60% LiCl Absorptions 20$ LiBr-808L101 ectrum LiCl Abscrptions 20$ LiBr-80 for for for for for for for for for frequencies for LiBr-NaBr spectrum for 79$ LiBr-21% LiBr . . . . . . 97$ LiBr-31 NaBr 90$ LiBr-10% NaBr 83$ LiBr-17% NaRr 50$ LiBr-50$ NaBr 30$ LiBr-70$ near 211 LiBr-79$ NaBr 10$ LiBr-90$ NaBr NaBr IIIIII films L101 (Initial) for (Final) for (Initial) for (Final) for ectrum (Initial) for (Final) for #1 #2 “3 #4 #5 #6 FIGURE 23. 2b. 25. 26. 2?. 28. 29. 30. 31. Dispersion Absorption Absorption Absorption Absorption Absorption Absorption Absorption frequencies for LiCl-LiBr films spectrum spectrum spectrum spectrum spectrum spectrum spectrum for 97.5% NaI-2.5% KI for 95% NaI-5% KI . . for 90% NaI-10% KI . . for 85% NaI-15% KI . . for 25% NaI-75% KI . . for 9% NaI-91% KI . . for 5% NaI-95$ KI . . Dispersion frequencies for NaI-KI films . APPENDIX FIGURES FOR PURE FILMS 32. 33- 34. 35. 36. 37. 38. 39. no. #1. 42. 43. an. #5. #6. #7. Absorption Absorption Absorption Absorption Absorption Absorption Absorption Absorption Absorption Absorption Absorption Absorption Absorption Absorption Absorption Absorption spectrum spectrum spectrum spectrum spectrum spectrum spectrum spectrum spectrum spectrum spectrum spectrum spectrum spectrum spectrum spectrum for LiCl . . . . . . for Lil . . . . . . for NaF . . . . . . for NaCl . . . . . . for NaI . . . . . . for KF . . . . . . for KCl . . . . . . for KBr . . . . . . for KI . . . . . . for RbF . . . . . . for HbCl . . . . . . for RbBr . . . . . . for RbI . . . . . . for CsF . . . . . . for 0301 . . . . . . for CsBr . . . . . . um Page #7 49 50 51 52 53 5h 55 56 66 67 68 69 7o 71 72 73 7h 75 76 77 78 79 80 81 CHAPTER I INTRODUCTION Sir Isaac Newton's classic work of 300 years ago revealed the composite nature of white light. The many investigations since then have divided the electromagnetic spectrum into regions based on frequencies or wavelengths. Each of these regions has become the basis for a branch of the science of electromagnetic spectroscopy, wherein the scientist studies the energy levels of a material system through the interaction of electromagnetic radiation with it. Infrared radiation, usually defined as the region between wavelengths TM - 1000fl, or wavenumbers 10,000 cm'l- 10 cm'l, largely characterizes the interaction with the more massive and larger basic units of matter such as molecules and ions either individually, or as they are found collectively in gases, liquids, and 5011ds. Our understanding of the interaction of electro- magnetic radiation with solids is far from complete. The collective system of particles making up a solid has held the theoreticians at bay, and we have no rigorous theory of absorption even for the simplest types of solids. Nor is there a systematic experimental study of this interaction. In our laboratory we have been concerned with experimental and theoretical investigations of the interaction between electromagnetic radiation and crystal- lattice vibrations in the region where the photon energies 1 ({[‘ll\l(‘ll\l'l\l|\ are comparable with the phonon energies. In searching for a system where this interaction is strong, we were led to ionic crystals as were Czerny (1) and his followers some 30 years ago. The alkali halides, in particular, are excellent materials for a systematic investigation of the photon-phonon interaction, because of their large induced electric-dipole moments and simple structure. In the absence of a rigorous theory we choose for our first-order model the simple picture of ions as charged mass points interconnected by approximately harmonic forces. This simple model needs to be improved to account for the shape of the absorption spectra, but refinements soon become complex and speculative. We have attempted to test these models in work carried out earlier in our laboratory by W.B. Zimmerman (2), R.H. Misho (3), and C.M. Randall (4), who have varied isotopic composition and temperature as experimental parameters in studies of infrared transmission through thin films of Lil-I and LiF. The frequency of the maximum absorption by thin films of the ionic crystal is designated as the infrared dispersion frequency. The work of Zimmerman (2) and Misho (3) has shown that this characteristic frequency is essentially proportional to the reciprocal of the square root of the average reduced mass for the LiF films composed of different proportions of the isotopes Li-6 and Li-7 in combination with F-19. But in similar studies with H-1 and D-2 in combination with Li-6, an unexpectedly large shift in the dispersion frequency was observed for a small percentage of LiD in LiH. J.R. Hardy (5) has recently published a theoretical explanation for this phenomenon. He suggests, moreover, that alkali-halide mixed crystals might produce similar anomalous shifts in the dispersion frequency when a few per_cent of the lighter host ions are replaced by heavier impurity ions. The temperature dependence of the dispersion frequency is not taken into account in any simple model. Randall (4) has made a careful experimental study of this relationship for LiF from room temperature down to liquid-nitrogen temperatures. His results agree well with an effect estimated from Szigeti's relationship (6) between the dispersion frequency and the fundamental crystal-lattice parameters. A As might be expected, the absence of an adequate theory makes it difficult to get meaningful insights from the shapes of experimental absorption curves. Randall (4) has extracted an experimental half-width parameter from his data on LiF. So far as isotopic mass is concerned he found no significant differences in this parameter for Li6F and Li7F; he has observed a dependence on temperature, however, which needs further investigation. The effect of isotopic mixtures is to give much broader 4 absorption bands than in pure films. The present thesis consists of two series of experimen- tal studies. The first part of the thesis is the determina- tion of the dispersion frequencies for all of the alkali halides with NaCl structure. This study includes the determination of the dispersion frequency for Lil for the first time, and the first determinations for LiCl, LiBr, KF, RbF, and CsF by transmission measurements. This work provides a complete tabulation of NaCl-type alkali- halide dispersion frequencies. This study of pure films, moreOver, serves to establish the soundness of the experimental technique, the purity of the materials, and the validity of the analysis. The second part of the thesis is a study of the infrared absorption of some films made from "pseudoisotopic" mixtures of alkali halides in which one alkali metal (or halogen) is replaced in part by another. The object of this study was to test this conception of "pseudoisotopicality" for the systems LiCl-LiBr, LiBr-NaBr, and NaI-KI, and to look for other effects due to finite concentrations of lattice impurities, as suggested by Hardy (5). CHAPTER II EXPERIMENTAL APPARATUS AND TECHNIQUE The experimental method was practically the same for both the pure films and the mixed films. Any differences in techniques or apparatus will be speci- fically noted. finial—e mung All of the alkali halides studied in this work are hygroscopic to some degree or other. Consequently, certain precautions were taken to minimize absorption of water vapor from the atmosphere. First, the materials were stored in desiccators open to room atmosphere only during the brief periods necessary to load evap- orator boats. To prepare mixed samples of desired com- position, suitable amounts of pure materials were weighed and mixed in a dry box charged with dry argon. The amounts were weighed in a single-pan balance sensitive to 0.1 mg. The samples were mixed with an agate mortar and pestle, and then placed in weighing bottles which after sealing were removed from the dry box and placed in desiccators. All of the alkali halides used in this study were commercially obtained high-purity chemicals. Wat rtinAEEarsm A commercial evaporation system was used to prepare the films. The pumping system consists of a 15-cfm mechanical pump backing a 4" oil diffusion pump, with a chevron-type liquid nitrogen baffle between the diffusion pump and the base plate. This system is capable of evacuating the bell jar to a pressure of SfITorr within 30 minutes. The base plate is equipped with high-current feedthroughs and with two combination rotary-translational- motion feedthroughs. Currents up to 250 amp are supplied from a low-voltage transformer fed from a 15-amp variable autotransformer. One of the secondary leads of the low- voltage transformer served as a primary vdnding for an instrument transformer which monitors the current through the boat. ‘ The experimental set-up for evaporation is shown in the schematic diagram of figure 1. The films were maintained i5 Egggg in two identical sample cells throughout the period of study. These cells, designed by W.B. Zimmerman, are described in detail by R.H. Misho (3). For the low-temperature studies, the substrate was mounted in a liquid-nitrogen container inside the vacuum cell. Figure 2 shows a cut-away view of the sample cell, with the liquid-nitrogen sample holder raised to clarify the construction. The top window was sealed to an O-ring by a brass holder as shown in figure 1. Throughout this study the material for the windows and the substrate was high-density polyethylene 0.40" thick. The second window, to be sealed after evaporation, was (’f.“ GLASS BELL JAR 90‘ RING SEAL V \ \ s s \ \—50AT \ \ [214 [4 /7////z/W//. Al l\_l \-x'l l I L__J PUMPING SYSTEM EVAPORATION SYSTEM Figure 1 8 Vacuum Valve [13»: o-a Casing Liquid Nitrogen Container , ) Window ,r’ SAMPLE CELL CROSS-SECTION Figure 2 placed in a holder mounted'on one of the rotary feed- throughs in the vacuum system. The entire sample cell was aligned for the proper sealing of this window, and the cell was then secured by means of a mounting bracket rigidly mounted to the base plate. Film Egepgrgtion Small quantities of the material to be evaporated were placed in the boat. Each boat was made of molybdenum and mounted on an insulating support which in turn was mounted on the second rotary feedthrough of the vacuum system. The boat was connected to the high-current terminals in the base plate. The system was then evacuated, and the window mount on the rotary feedthrough was placed between the boat and the substrate mounted in the sample cell (see figure 1). This window mount served as a shield for the substrate during the period of preheating before evaporation. The preheating of the material in the boat was monitored by means of the pressure of the system as measured on an ion gauge. The pressure usually stabilized after heating for a few minutes. This period of outgassing is very important when dealing with the hygroscopic materials used in this study. Without this precaution some of the evaporant sputters out of the boat, and useful films are not obtained. After the period of preheating, the current to the boat is raised until the powder melts. As part of this study, the substrate 10 shield was removed at different times during evaporation. The resulting films from the different portions of the evaporation produced no observable differences in their transmission spectra. The period of evaporation was approximately 20 seconds with the boat 10 cm from the substrate, and with a boat current of 100 amp. After the current to the boat was turned off, the window holder was rotated into position and the window was pressed firmly against the O-ring in the sample cell (see figure 1). Air was admitted to the bell jar. The pressure difference between atmosphere and the inside of the sample cell sealed the polyethylene window in its position, thus maintaining the film in a vacuum inside the sample cell. The cell was then removed from the mounting bracket in the evaporator and placed in the sample compartment of the Perkin-Elmer 301 spectrophotometer. Hose connections were made between the sample cell and forepump, so that the cell could be pumped on at any time during the experiment. With this arrangement the pressure inside the sample cell could be maintained below 10"3 Torr throughout the course of an experiment. The output from a copper-constantan thermocouple was fed into a Daystrom-Weston multiple-station self-balancing recording potentiometer to measure the temperature of the substrate for the low—temperature runs. The thermocouple junction was clamped firmly against the high-density 11 polyethylene substrate. Randall (4) ascribes to similar thermocouple temperature measurements an accuracy of t 1 deg-C at liquid-nitrogen temperature, and a higher accuracy at room temperature. TransmissiQn-Spectra Measurements The transmission spectra of the films were obtained with a commercial double-beam far-infrared spectrophoto- meter, the Perkin-Elmer Model 301. A diagram of the optical path of the instrument is shown.in figure 3. Between the source at I and the Golay detector, several of the reflection elements, the transmission filters at F3, and the crystal choppers may be changed in order to isolate a narrow band of the electromagnetic spectrum for dispersion by the grating G1. The mechanical drive for the grating is designed so that the frequency of the radiation passed by the monochromator is directly ,proportional to the number of drive-shaft turns, which is based on an arbitrary scale of 100 "drum turns" per revolution. The "drum turns" scale was calibrated in terms of frequency for each grating by operating the instrument in the single-beam mode, and measuring the positions of the absorption bands of atmospheric water vapor. The frequencies of these bands are tabulated in the literature (7), and a straight line between these values and the experimental data was fitted by the Figure 3. 12 Optical path of the Perkin-Elmer 301 far- infrared spectrophotometer. Reflection elements on F1, Fl', and F2 may be changed from outside the instrument. Mirrors M4, M4', and M12 along with the choppers may also be changed to isolate a band of the electro- magnetic spectrum for dispersion by the grating G1 before being detected by the Golay cell near M22. m 933% mmEEOHOIn—Othmdm emu/Diz— - z20. with greater importance of these two factors in the theorectical picture of our system. We will have occasion later to make use of this correlation. 24 From the classical theory of dielectric constants for ionic crystals, Szigeti (6) has developed the following equation relating the dispersion frequency to other experimental parameters: (3) 60—6,.=(e,.+2)1[4TrN(2e)2]/9M a): where €¢.is the high-frequency dielectric constant, €o is the low-frequency dielectric constant, oi.is the infrared dispersion frequency, N is the number of ion pairs per unit volume, Ze is the ionic charge, and M is the reduced mass of the positive and negative ion pair. Equation (3) is not satisfied by the experimental data. Consequently Szigeti (6) introduced an effective charge e* in place of e in this relation. Then the ratio of e*/e is given by (4) (e*/e)2= 9 Rut (e.— £..)/41TN e1(e..+ 2)‘ (for z =1) Thus the difference between the ratio e*/e and unity serves to show the discrepancy of the classical model with respect to the experimental data. Table II compares the ratios of e*[e as calculated by equation (4) with this ratio as predicted from other models. The discrepancies between experimental data and the simple theoretical models have been confirmed by previous studies. Jones 25 al.(10), in particular, have shown that these differences do not disappear even at liquid-helium temperatures where the models are more likely to be valid. Material LiF LiCl LiBr LiI NaF NaCl NaBr NaI KF KCl KBr KI RbF RbCl RbBr RbI CsF 25 TABLE II Comparison of e*/e Values Szigeti 0.81 0.77 0.77 0.55 0.95 0.74 0.70 0.70 0.88 0.80 0.77 0.71 0.95 0.83 0.83 0.76 0.86 Mean deviation From Szigeti value Havinga 0.77 0.67 0.71 0.52 0.85 0.68 0.71 0.64 0.83 0.80 0.81 0.74 0.71 0.76 0.80 0.76 0.89 0.056 Dick & Overhauser (e*/e)extreme e*/e 0.91 0.92 0.91 0.90 0.93 0.91 0.89 0.89 0.98 0.93 0.93 0.91 1.05 0.95 0.92 0.93 0.134 0.88 0.90 0.90 0.88 0.86 0.84 0.82 0.83 0.87 0.84 0.84 0.82 0.88 0.84 0.83 0.85 0.082 26 There have been a number of theoretical discussions concerning the origin of these deviations of e*/e from unity, and we now discuss our results in light of these. The three main factors affecting the value of e*/e that are not accounted for in the simple theory are 1) ionic overlap, 2) ionic distortion, and 3) anharmonic forces. The shell model, first proposed by Dick and Overhauser (12), is an,attempt to correct for overlap and ionic distortion in determining the ratio of e*/e. Havinga (13) has modified this model, and in Table II the theoretical values of e*[e based on each of these papers are compared with those determined from the experimental data and the Szigeti formula. The shell model may be qualitatively understood in the following way. An ion is assumed to consist of a spherical shell of n outermost electrons and a core consisting of the nucleus and tightly-bound inner electrons. In an applied electric field the shell is assumed to maintain its spherical shape, and to move with respect to the core. A harmonic restoring force acts between the core and the shell. Now, the shells of the positive and negative ions repel each other and tend to become displaced with respect to the ion cores because of this repulsion. This displacement represents a short-range polarization of the ions. Since the restoring force in the larger negative ions is in general weaker than that 2? in the positive ions, we expect the short-range polar- ization of the negative ion to exceed that of the positive ion (if shell charges are the same). Thus there is a net dipole per ion pair directed opposite to the applied field, and this contribution serves to lower e*/e (i.e. to reduce the total dipole moment) below unity. The results in Table II show that the shell model accounts for some of the disagreement between the experimental data and the simple theory. Havinga's values are in general closer to the experimental values, but one would hope for still better agreement. We note a correlation between larger values of EZDI in Table I, and the larger deviations of e*le from unity in Table II. This correlation, which is consistent with taking ionic overlap effect as one of the origins of the damping, might prove to be a valuable area for further studies, in which one would seek an inclusive theoretical description of the interaction of electromagnetic radiation with ionic crystals. Him-Balm Raul—ts. Three systems of mixed alkali-halide films were studied: LiBr-NaBr, LiCl-LiBr, and NaI-KI. Films were made of several different molecular percentages for each of the three systems. The frequency of minimum transmission was determined for each film as previously described. This frequency will hereinafter be called the mixed film 28 dispersion frequency. These dispersion frequencies are reported along with the values for the pure-film dispersion frequencies for each of the systems studied. Specific comments will be made for each system in turn, and a general discussion for all of the mixed-film results will follow. LiBr-NaBr System Figures 6 to 14 show spectra for various compositions of the LiBr-NaBr system. A plot of the dispersion frequencies for various compositions is shown in figure 15. There are three observations to be made for this system; first, the absorption maximum becomes broader and more poorly defined as the composition of the melt approaches 50%950%; second, the dispersion frequency changes more for a small percentage of NaBr in LiBr than it does for the same percentage LiBr in NaBr; third, a small percentage of NaBr in LiBr changes the shape of the spectra much more than the same percentage of LiBr in NaBr (cf. figures 8 and 13). mm Figures 16 to 22 show spectra for different compositions of the LiCl-LiBr system. In figure 23 both the initial and the final values of the dispersion frequency are plotted for each of the different mixed films. The initial value of the dispersion frequency is that taken from the first spectrum obtained following 29 Mada o shaman “annoy hososwenh on“ own on“ com omH oma o omw mam _ a _ _ _ I cm I on as a I.. CW 1 om _ _ L _ \_ a 00H 3O OON undu— finlundfl KO SIR: 8:25lo s. shaman oma one and owe one oea ona _ _ _ _ _ a O fl I on I I 2. as a F I 8 P p b _ _ _ OOH 31 I. m chomam Hmez XOHIHmAq mom AHIEOV hoooououh cow oma oma and cod and ova oma _ 1 _ 1 _ _ o l nuom I. Inoc $3 a l .Iom .I Ilom r _ _ _ _ r I I\IIIII CCH m ouomam some 1\4:» a. :51 AHIEUV avocados: omH omH 05H 00H OmH ova one owa _ _ _ L _ . _ 0 ll. IL ON I. I. or n so a I. I1 om _ _ L _ a r _ IIIIII ooa 100 33 80.. 60.. ’1' (5‘) “Or-— 20- J l 120 Figure 10 130 140 150 Frequency (cm'l) 50$ LiBr-50% NaBr 160 170 1III4‘III .1 441‘: 14-1 1.1 4 1... (I I I E» 14.41 «I 100 34 80 — 'r (5‘) 20’ 0 120 Figure 11 130 140 150 Frequency (cm'l) 30% LiBr-70% NaBr 160 170 35 10 80 —— .— 60— _ r (S) 20 —- .— 0 I I I I I 120 130 140 150 160 170 Frequency (0111"1 ) 21$ LiBr-79% NaBr Figure 12 100 36 got 60— T (1) 20r- I l I l 120 Figure 13 130 140 150 160 Frequency (cm'l) 10% LiBr-90% NaBr 170 37 100 80,— 60- T (5) 40— 0 120 130 140 Frequency Figure 14 NaBr 1 (cm 50 -1) 160 170 I70 ISO u,(cm") I50 — / ' ff?) '— / / / _ / 7/ — / / / // I40 — , — / x—x—-xm x . Z _ '30 I I I I I I I I I LIBI’ O 50 IOO NaBr IOO SO 0 . Figure 15 ._ 38 MOLE % 39 evaporation of the film. Instead of lying between the dispersion frequencies of the pure films as expected, this initial frequency is much higher than that of pure LiCl films. After a period of from several minutes to several hours during which the film is maintained ;p v c , a new spectrum appears, revealing the dispersion frequency shifted to a lower value that lies between the dispersion frequencies for pure films. Such a final equilibrium value for the dispersion frequency was found for all of the films having the melt compositions 80% LiCl- 20% LiBr, 60%-40% LiCl-LiBr, and 40%-60% LiCl-LiBr. The 21% LiCl-79% LiBr composition never pro- duced a spectrum with such an initially high value of the dispersion frequency. The spectra (see figures 16 and 17) show that the initial absorption peak is usually better defined than the final one. Moreover, the absorp- tion peak is broader for films from 60%r40% combinations than for 80%—20% combinations. N - I m Several spectra for different compositions of the NaI-KI system are shown in figures 24 to 30. Each figure shows spectra at room temperature (c-300°K) and liquid-nitrogen temperature (~110°K film temperature) for the same film. A plot of the dispersion frequencies for various compositions at room temperature and liquid- nitrogen temperature is shown in figure 31. Since this 4O 60—- r (5‘) 40—- 0 I I I I 'I 150 I70 190 210 230 Frequency (cm-1) 79% LiBr-21% L1C1 Figure 16 41 100' 80 _. 60— T (S) 40— 20 —— o I I I I I 225 245 265 285 305 Frequency (cm-1) (Initial) 60% LiBr-40% LiCl Figure 17 325 42 100 80 h— __ 60 —— —_ T ($) 40 —— —- 20 —— __ o I I I I I 150 170 190 210 230 Frequency (cm-1) IFinal) 60$ LiBr~40$ L101 Figure 18 43 80 - 60 F- T (S) 40 - 20 - 0 I I I I I l 225 245 265 285 305 325 Frequency (cm'l) (Initial) 40$ LiBr-60$ L101 Figure 19 100 44 60_ T Is) not. 20 —- 150 Figure 20 170 190 210 Frequency (cm'l) (Final) 40% LiBr-60$ Licl 230 F182 20 100 45 80 _. 6O —- T (%) 40 —- 20 —- 245 Figure 21 265 285 305 325 Frequency (cm-1) (Initial) 20% LiBr-80% LiCl 345 46 100 80 — 60 _ T (S) 40 - 20 - I l I l l 150 170 190 210 230 Frequency (cm‘l) (Final) 20% LiBr-80% L101 Figure 22 300 250 00, (cm") 200 LIGI 4? I'x // ,x’ x/ x ' Initial Values A Final Values / /A"‘"""“ A/ O LiBr IOO Figure 23 50 50 ' MOLE °/o 48 system was the only one studied at low temperatures, it is hnportant to note the increased sharpness of the peaks and the upward shift of the dispersion frequency at low temperatures. The spectra obtained from the different compositions of this system show a broadening of the absorption peak as the melt mixture approaches 50%-50% both at room temperature and at liquid-nitrogen temper- ature. In this system there also appears to be a greater broadening with the 5% KI-95% NaI than with 5%NaI -95%KI mixture. (cf. figures 25 and 30) 49 100 80 — — 60 — T (Z) 40 - 20 — 90 100 110 120 130 Frequency (cm'l) 97.5%NaI-2.5$KI Figure 24 The solid line represents room temperature data, and the broken line the 110°! data. T (S) \ I \\\ I], I 4o.— ‘ I — \\ 1’ \‘_” 20-— _ Q I I I 100 110 120 130 Frequency (cm'l) 95%NaI-5SKI Figure 25 The solid line represents the room temperature data, and the broken line the 110°K data. III I III i 51 100 80 —- _. T (Z) o I I I 100 110 120 130 140 Frequency (cm'l) 90%NaI-10ZKI Figure 26 The solid line represents room temperature data, and the broken line the 110°K data. 52 100 80 L ._ 6O _ — T (f) o I I I I 100 110 120 130 140 Frequency (cm‘l) 85%NaI-155KI Figure 27 The solid line represents rgom temperature data, and the broken line the 110 K data. Fig 53 100 80 _, 60 — r (S) 40-— 20-— \ \" "‘-’.‘\"§ - n .’ 90 100 110 120 Frequency (cm'l) 25%Na1-75SKI 130 Figure 28 The solid line represents room temperature data, and the broken line the 110°K data. 54 100 T (S) o I I I 90 100 110 120 130 Frequency (cm'l) 9fNaI-91‘KI Figure 29 The solid line represents room temperature data, and the broken line the 110°K data. 55 100 80 — 60-— T (I!) 40-— 20r — o I I I 90 100 110 120 130 Frequency (cm'l) 5%Na1-955KI Figure 30 The solid line represents room temperature data, and the broken line the 110°K data. .. 7‘ I20— / .. / _ .. / ’9‘- / _ 1/ x "5 - / fl) ,/ /' _ ‘_ / x //L x—. - .-_ _. ,,/ _ _ / / ./ A /x / / /_ .. 1 , / A x "/4 / .- I -I '4 f/ / w.(cm ) no .I A _ A, -‘ / // - I ,A" * ~ ~ ”A’ I. /' / L - / )6- / _ IOS‘L I " _ HI x IIO°K - 7 A 300°K _ I11 _ IOO ' I ' ' I l I I | Ncl o 50 '00 KI I00 50 0 I-"I , I J MOLE % 5 FIG llI I'IIJ‘IIII IIIIIIII‘I‘IIIIIIII 57 General Discussion TWO aspects of the experimental results need discussion. First, the dispersion frequency and its dependence on composition and temperature of the films; and second, the shape of the spectra as it changes with composition and temperature of the film. Infrared pispersion Frequency We have defined the dispersion frequency as the frequency at the minimum of the transmission spectra. The values of the dispersion frequencies are plotted for each of the systems studied in figure 15 (LiBr-NaBr), figure 23 (LiBr-LiCl), and figure 31 (NaI-KI) as a function of the composition of the melt in the boat during evaporation. First it is in order to check on the pseudoisotopic character of these systems. The simple model of lattice vibrations shows that the infrared dispersion frequency is proportional to the inverse of the square root of the isotopic mass. Actually, comparisons should be made at the same reduced temperature IQ), where<9 is some character- istic temperature. The dispersion frequencies vary only slightly with temperature, however, and we will make comparisons at the same actual temperature. Comparison of the ratios of the dispersion frequencies CU/Q. with the appropriate reduced mass ratios ORDIOW are shown in tables III through VIII. It is clear that our naive TABLE III Effect of composition on dispersion frequency for NaI-KI films with w. and In. from NaI as reference. Composition 58 NaI 95%NaI-55KI 90$NaI-105KI 80$NaI-2ozx1 60$NaI-40$KI 20%NaI—80ZKI 10%Na1-9oxx1 5%NaI-9SZKI KI TABLE IV Effect of composition on dispersion frequency for NaI-KI films with w. and ,4. from KI as reference. a LEI-11 ”41. (It)?1 0" 711),]; 115 1.00 4.42 1.00 112 0.97 4.48 0.99 110 0.96 4.54 0.97 109 0.95 4.66 0.95 108.5 0.94 4.89 0.90 108 0.94 5.29 0.84 105.5 0.92 5.38 0.82 102.5 0.89 5.42 0.81 101 0.88 5.48 0.80 Compo s it ion Q (913' 1 ) u"/40. (’1 IV: (“a/M )Il‘ KI 101 1.00 5.48 1.00 5%NaI-955KI 102.5 1.02 5.42 1.01 10%NaI-905KI 105.5 1.04 5.38 1.02 20%NaI-805KI 108 1.07 5.29 1.04 40%NaI-6OSKI 108.5 1.07 5.10 1.08 80%NaI-20SKI 109 1.08 4.66 1.18 90%NaI-10SKI 110 1.09 4.54 1.21 95%NaI-5xx1 112 1.11 4.48 1.22 NaI 115 1.14 4.42 1.24 TABLE V Effect of composition on dispersion frequency for LiBr-NaBr films with 0% and [A from LiBr as reference. Composition 59 LiBr 90$L18r-10fiNaBr 83%LiBr-17%NaBr 75%LiBr-25SNaBr 30%LiBr-701NaBr 21%LiBr-79SNaBr 10%LiBr-905Na3r NaBr TABLE VI Effect of composition on dispersion frequency for LiBr-NaBr film with co. and [A from NaBr as reference. Composition 1.11635) “/65. (MIA (”WI/2 171 1.00 2.53 1.00 158 0.92 2.80 0.90 157 0.92 2.94 0.86 152 0.89 3.10 0.82 139 0.81 3.85 0.66 139 0.81 3.98 0.64 137 0.80 4.11 0.62 135 0.79 4.22 0.60 NaBr 10$LiBr-9OSNaBr 21$L1Br-79ZNasr 30%LiBr-70SNaBr 75%L1sr-251NaBr 83%LiBr-17%NaBr 90$L13r-105Nasr LiBr w ( 2,!- 1 1 w/w, 0* )1/1 I (“7/ I1 )7; 135 1.00 4.22 1.00 137 1.02 4.11 1.03 139 1.03 3.98 1.06 139 1.03 3.85 1.10 152 1.13 3.10 1.34 157 1.16 2.94 1.43 158 1.17 2.80 1.50 171 1.27 2.53 1.67 TABLE VII Effect of composition on the dispersion frequency for L101-LiBr films with 01.and A“ from LiBr as reference. Composition 60 LiBr 79%LIEr-215L101 60%LiBr-40SL101 40$L13r-601L101 20%L18r-80ZL101 1101 (0 940. (III!1 05446 171 1.00 2.53 1.00 174 1.02 2.51 1.01 176 1.03 2.50 1.01 181 1.06 2.48 1.02 189 1.11 2.45 1.03 201 1.18 2.41 1.05 TABLE VIII Effect of Composition composition on the dispersion frequency for L101 20%L18r-805L101 40%LiBr-60%LiCl 60%L13r-405L101 21%L13r-79ZL101 LiCl-LiBr films with 6.). and )4. from 1.101 as reference. (0 “70. (“IL (“VIII/2 201 1.00 2.41 1.00 189 0.94 2.45 0.98 181 0.90 2.48 0.9? 176 0.88 2.50 0.96 174 0.87 2.51 0.96 171 0.85 2.53 0.95 LiBr 61 pseudoisotopic assumption is not supported by these data for pure films. We still might expect, however, that for small amounts of impurity atoms replacing host alkali-halide atoms, we would find the reduced mass to be the dominant factor in determining the dispersion frequen- cy for the mixed systems. In the tables we find reason- able agreement for films from melts containing small percentages of impurity atoms replacing host atoms. Films from mixtures containing a few percent of the heavier impurity atoms tend to have larger deviations from this pseudoisotopic characteristic for all of the systems stud- ied. Although this shift of dispersion frequency is qualitatively in support of Hardy's (5) suggestion, no large shift of the dispersion frequency occurs for these small concentrations of impurities, as was observed for the LiH-LiD system (3). We note also that the frequency ratio is higher than the appropriate reduced-mass ratio for the LiBr-NaBr system and the LiBr-LiCl system when the minority component is the heavier constituent. In our simple model this relation implies a greater force constant or restoring force for the mixed films. For the NaI-Kl system the frequency ratio is higher than the appropriate reduced- mass ratio when the minority component is the lighter NaI. From the data of figure 31 we can determine the ratio of the dispersion frequency at 110°K to the dispersion frequency at room temperature for each of the combinations of the NaI-KI system that were studied. This ratio is 62 calculated to be 1.05 for each of the combinations. The constancy of this ratio is consistent with the pseudo- isotopic assumption made for small percentages of one alkali halide in a host film. For in this model, the reduced mass, which is independent of temperature, is the dominant factor in determining the dispersion frequency of the mixed film. Absogption Spectra Spapp Although there is no complete theory for the structure of the absorption bands, we may gain some insight from observed differences in the shapes of the mixed film spectra as determined by composition and temperature. As pointed out before, a 97%LiBr-3%NaBr mixture, and similarly a 95%NaI-5%KI mixture, produce a much broader absorption hand than does the 5%NaI-95%KI mixture. In both the LiBr-NaBr system and the NaI-KI system, a small percentage of the heavier component put into the lighter host produces a broader absorption band than the reverse combination. This observation may be interpreted in the following way. This broadening of the absorption band is accompanied by a non-isotopic shift in the dispersion frequency. This shift in turn may be interpreted as evi- dence of an anharmonic perturbation on our harmonic binding force. One of the many suggestions made to account for absorption band widths is that such anharmonicity would indeed give rise to secondary structure in the infrared absorption spectra. 63 In summary, this study has demonstrated the feasibility of getting meaningful data for all the alkali halides in pure form, and has pointed out promising areas for mixtures of alkali halides. There appears to be a correlation between the larger values of the damping parameter and the larger deviations of the e*/e Szigeti ratio from unity. This correlation deserves further study, both experimentally and theoretically. The information contained in the shape of the absorption spectra remains untapped. In the mixed-film spectra of this study there was some systematic variation of spectra shape as a function of both composition and temperature. As yet, however, we have no good theoretical interpretation of these observations. FUrther investigations of mixed films and pure films at low and high temperatures would provide further insight into the temperature dependence of the dispersion frequency and absorption spectra shape. Data from other mixtures of alkali-halides con- taining no common constituents would provide additional information concerning the pseudoisotopic character of alkali-halide systems. For a thorough check of Hardy's (5) theoretical treatment of isotopic defects, an experimental study of the NaHrNaD system is needed. 2 34.5 6 11. 12 13. 14. 64 References R. B. Barnes, and M. Czerny, Z. Phy sik 72, 447 (1931); R. B. Barnes, Z. Physik 75, 723 (1932). W. B. Zimmerman, Ph.D. Thesis, Mich. State. U. (1960) R. H. Misho, Phw D. Thesis, Mich. State U. (1961) C. M. Randall, Ph.D. Thesis, Mich. State U. (1964) J. R. Hardy, Phys. Rev. 5136, 1745 (1964). B. Szigeti, Proc. Roy. Soc. 5294, 51 (1950). H. M. Randall, D. M. Dennison, N. Ginsburg, and L. R. Weber, Phys. Rev. 5;, 160 (1937). K. N. Rao6 R. V. deVore and E. K. Plyler, J. Res. N. B. s. 675, 351 (1963). M. Hass, J. Phys. Chem. Solids 24, 1159, (1963). G. 0. Jones, D. H. Martin P. A. Mawer, and C. H. Perry, Proc. Roy. Soc. A26 , 10 (1961). u. w. Hohls, Ann. d. Physik g9, 433 (1937) 90 %.9Dick, Jr. and A. W. Overhauser, Phys.Rev.112, 15 E. E. Havinga, Phys. Rev. 112, 1193 (1960). M. Born and K. Huang, 1954, Dypamical Theogy pg ngstal Lattices, Oxford, Clarendon Press. APPENDIX Adjusted Transmission Spectra for Pure Alkali-Halide Films 100 66 80 _. 60 —— T (i) 40 _. 20 _. 180 Figure 32 190 200 210 220 Frequency (cm-1) L101 230 Ii. Q! ’Afifng‘ 67 100 I I I I 80 I— _ 60 -— _ T (5‘) 40 L- -- 20 —- ._ o I I I I 120 130 140 150 160 170 Frequency (cm'l) L11 Figure 33 68 100 80 —- __ 6o _. _. T (S) #0 - - 20- J o I I I I I 210 220 230 2&0 250 260 Frequency (cm‘l) NaF Figure 3b 100 69 80 - 60 —- T (f) #0 —— I I I I 1uo Figure 35 150 160 170 180 Frequency (cm'1) NaCl 190 70 100 T (S) o I I I I 100 110 120 130 140 Frequency (cm‘l) NaI Figure 36 The solid line is room temperature data and the broken line is 1100K data. 71 100 I I I I 80 _ _ 60 a. -d T (It) 40 _ + 20 -— _ o I I I l 170 180 190 200 210 220 Frequency (cm-1) KF Figure 3? 72 80.. 60_— T (%I 40-— 20-— 0 , 120 Figure 38 130 140 150 Frequency (cm'l) KCl 160 73 100 80- 60— T (S) 20h— _. o I I I I 100 110 120 130 140 Frequency (cm‘l) KBr Figure 39 The solid line is room temperature data and the broken line is 110°K data. 74 100 80-—- 60_ T (S) \ 20 —— .— o I I I I 80 90 100 110 120 Frequency (cm'l) KI Figure #0 The solid line is room temperature data and the broken line is 110°K data. 100 75 80 —- 60 .- T (5‘) 40 -— 20 - 130 Figure #1 1&0 150 160 170 Frequency (cm‘i) RbF 180 76 80- .— 60.. T (5‘) “Or 20—— 1:) 100 110 120 130 140 Frequency (cm'l) RbCl Figure 42 The solid line is room temperature data and the broken line is 110°K data. If I I I 80 _ _ 60 _ _ T (S) no - _ 20 — _ o I I I I 70 8O 90 100 110 Frequency (cm'l) RbBr Figure #3 100 80 —— 60 _ T (I!) 20 F' 6O 70 80 90 100 Frequency (cm-1) RbI Figure 4h 79 100 l I I 80 — _ 60 _ _ T (S) no — _ 20 _ _. o I I I 110 120 130 140 150 Frequency (cm'l) CsF| Figure #5 90 100 110 120 130 Frequency (cm'l) 0301 Figure 46 The solid line is soon temperature data and the broken line is 110 K data. ~(4’V—V. wt_ 81 BOF- _. 60—- T (i) 20—- o I I I 60 70 80 90 100 Frequency (cm-1) CsBr Figure #7 The solid line is room temperature data and the broken line is 110°K data. ”rt .1. ‘3 .. IIIIIIIIIIII2IIIIIIIIIIIIIIIIII|IIIIIIIIIIIIIIIIIIIIIIIIIIIIIII